Thursday, 23 February 2012

What makes a good mechanical puzzle?

I found myself chewing this one
over a bit recently and before I knew it, it had started growing arms and legs
and turning into a blog post … it may be a bit philosophical, it will almost
certainly be heavily influenced by what I like and it will be my opinions –
feel free to have some of your own and share them if you’d like by leaving a
comment or three down below…

The topic seems to come up from
time to time on the usual puzzle forums and it’s always interesting to see the
variety of responses – there almost certainly isn’t ever going to be a single,
agreed answer. Heck, I doubt you could get firm agreement on what aspects
should even be considered, let alone their relative importance or how to
combine the various aspects that make them up!

For me, it’s about the joy of
discovering stuff – so my ideal puzzle starts out with something that seems
totally impossible and then takes you through a series of discoveries (“A-HA!”
moments) that slowly let you in on the secrets it holds until you finally open
it / close it / assemble it and reach your goal. So let’s unpack that a bit… with tongue firmly in my left cheek, I reckon:

Where:

PG is Puzzle Greatness (!)

GC is Goal Clarity (Scale: 1-3)

Ach is Sense of Achievement (Scale: 1-3)

El is Elegance (Scale: 1-3)

Att is Attractiveness (Scale: 1-3)

P is the number of Pieces

Ch is Level of Challenge (Scale -0.5 - 0.5)

AHA is the number of A-Ha! moments

X is the factor to allow for bonus points

It probably sounds obvious, but
it should have a clear goal – any
mechanical puzzle that needs a significant explanation of what the goal is, is
unlikely to be a really great puzzle – give anyone a scrambled twisty puzzle
and immediately they know that they need to get the colours on the faces
matched up … they might not know how to achieve some aspects of the solution
without consulting an algorithm, but everyone intuitively knows what to try and
do with them. (Yes, I know that it’s less obvious with some shape-shifters
where you might not be able to even recognise what the target shape should be,
but you get the point – stop trying to be difficult!) Multiple sequential
goals, each of which logically tees up the next are even better (and I’m
thinking of some of Pavel Curtis’ puzzles here where you uncover them
one layer at a time, a bit like peeling an onion).

When it comes to mechanical
puzzles, fewer bits are always
better than lots of bits. Making puzzles harder by adding pieces may make them
more complicated, but it doesn’t necessarily make them any better. Think of the
two-piece pyramid puzzle – two simple little pieces have to be combined to make
a tetrahedron (or pyramid, if you aren’t among friends!). There’s a real
elegance that comes from having a smaller number of simpler pieces to a puzzle
– in my books, some of the best packing puzzles have four simple pieces to fit
into a tray. Your brain tells you it should be simple – experience tells you it
isn’t!

I suppose there’s a temptation
to say that this rule wouldn’t apply to jigsaw puzzles (if you consider them
mechanical puzzles) – except I think it does apply, within reason …my favourite
jigsaw only has a couple of hundred pieces, but they’re mostly different shapes
and have whimsies scattered around the place – I can honestly say that I find
that one a ‘better’ puzzle than some of the 1 000-plus piece monsters I’ve had
a go at – and I don’t expect to ever get too keen on starting one of those 32
000-piece Ravensburger mega-puzzles! …but I can’t wait to get my hands
on a copy of the Four Colour Map Puzzle
from Artifact Puzzles and it only has 68 pieces … but just look at the shapes
of those pieces…

Good puzzles should provide at
least a reasonable challenge – they
need to keep you occupied for a bit at least (are they really puzzles if they don’t?) – they need to
earn some respect before they give up their secrets. I always find it a bit of
a let-down when I look at a new puzzle from a distance, decide what the goal
probably is and then take a guess at the likeliest solution only to find out
that’s exactly what it is when I pick it up and just apply the solution – and I
fully realise that it all depends on what you’ve seen before and how much
experience you have of solving mechanical puzzles, and that to some extent your
views will be influenced by when during your puzzling life you came across a
particular puzzle and how on-your-game you were when you first saw one – but I
guess what I’m really saying is that trivial puzzles with an obvious solution
aren’t likely to be high on the list of great puzzles in my books.

There’s probably a down-side if
puzzles provide too much of a challenge … I’ve spent hundreds of hours
(literally!) on a single puzzle spread over several months before I finally
cracked it –and trust me, the sense of achievement was pretty sensational – but
I don’t think there are many puzzles that I’ll invest quite that much time in.
There are other sorts of puzzles that (for me) take a lot of thought away from
the puzzle itself – so they tend to sit on my bookshelf above my desk for ages
– and every now and then I’ll take them down, try a couple of things and then
put them back and leave them alone for days or weeks at a time – Roger puzzles
fit this category rather neatly – I find they need you to try lots of things,
often unusual things, and they can be pretty devious little things … in fact at
the moment there’s a row of three of them that have been staring at me for
quite a while now … all unsolved, so far ….

Good puzzles give you a sense of achievement – and to some extent
I suppose that’s the flip-side of the previous point. Everyone (OK, we
puzzlers…) loves conquering a puzzle and getting the better of it – proving
that you’ve found the right technique to work out what the internal mechanism
must be to release that final catch and open the box – or be able to deduce how
to fit those shapes into that tray in a way that your brain wants to tell you
cannot be efficient enough.

Good puzzles give you “A-ha! moments”. Great puzzles give you
several of them. For me personally, these are the drug that makes solving
puzzles so addictive – that briefest little moment of insight that comes after
trial and error and thinking deep thoughts when suddenly there’s a tiny flash
of inspiration and an inkling that that
might actually work – the moment when the grin creeps across your face no
matter how jaded or experienced you are when you realise that you’re onto
something useful. That’s the real buzz of solving puzzles for me – that’s the
bit I remember best about solving puzzles … it’s that first time you spot
something behaving unexpectedly and then wondering why it did that, or
postulating a theory about what might be in there and then coming up with a way
of testing the theory, trying it and realising that it might actually be part of
the solution.

Great puzzles have an elegance to their mechanisms or their
solutions – think Cast Marble.
Maybe there’s an inner-engineer in me trying desperately to come out, but I
really appreciate elegant designs that don’t complicate things unnecessarily.
Implementations of the simplest means of achieving a particular mechanism /
trick or disguise are best. Bonus points for re-using things in unexpected ways
…

Call me shallow, but I like
puzzles to look attractive as well –
and I guess this is where we seriously start getting into the realms of
personal tastes! I really think that a beautifully made hardwood puzzle looks
inviting and displays well – I like the idea of puzzles that look good on their
own in a puzzle cabinet, ones that look a bit different and ones that show off
their creator’s skill and craftsmanship.

I also think some puzzles should
get bonus points for things like
having an extra little hidden compartment in a puzzle box beyond the main challenge,
or for being puzzler’s puzzles – where they’re specifically designed to use a
puzzler’s knowledge of similar puzzles against them finding the right solution
… often resulting in non-puzzlers who are unencumbered by “knowing what the answer should
be” being able to solve them faster than “real
puzzlers”.

12 comments:

Very clever! I see how your "X Factor" is a fudge factor that allows you to rate any puzzle as you please! :-)

Personally, I don't have much hope for any quantitative rating system. The reason is that some people love certain puzzles, others hate them and prefer others. In other words, there is no rating system that will satisfy everyone, or even come close. Even the same person may rate the same puzzle quite differently if considered 10 years apart. I think puzzle classification is much more likely to reach consensus and provide useful information.

You got me George! As my puzzle-mad-mate Kevin says, "Subtle as a brick!"

Totally agree with you that you cannot encapsulate that stuff in an objective, repeatable formula - we all change and there's no way of allowing for individuals' tastes properly ... perhaps the formula was just a cheap trick to sucker the mathematicians out there into reading the wordy bits? :-)

I am shocked that as a mathematical genius actuary you did not take into account the fact that elegance is inversely proportional to fourth root of the number of pieces!!

I loved this article and can see a whole lot of truth in your thoughts and (god help me!!) even he equation! I reckon that the Opening bat must score the highest on he puzzle greatness score! The number of Aha! Moments must be staggeringly high.

If a puzzle has zero AHA moments your score simplifies to 1+X! I myself either have few aha moments, or am merely stingy about awarding ahas. How many ahas does a Rubik's cube get? I say zero, but I suppose one could argue it is many.

...subtly George has exposed another of my little puzzle biases (I was trying to hide the fact that I wasn't a huge twisty fan and can't really do them - but now I've been outed!) - I'm not going to pretend that I meant it to simplify down to that if there were no A-Ha's, but it does sorta match my personal requirements for a GREAT puzzle. :-)

Loved the article but feel there is an element of the equation missing. That is PAF or Play Again Factor. Many puzzles, once solved, remain as such - solved. Others are fun to pick up again and again because they're fun to do so. I have resolved RevoMaze Blue and Bronze hundreds of times yet the silver I've only done twice! Not to say I don't like the silver, just it's not one I want to return to again and again.

Same with Super Cubi. It's easy to solve but I love flying quickly through the sequence and then reassembling.

In summary I think a great puzzle should also have the element of 'pick me up again and solve me!'